physicscarp
Explorer
Here is the situation:
In the game we are playing, characters may have a skill rank ranging from 1 to 20
, and to suceed at a task, the player must roll at or below his skill rank on a d20. Therefore the chance of success (S) for an event is S = n/20.
Now, during the game, a player may spend a hero point to either...
1) add +4 to his original skill level or
2) reroll a failed roll
I'm wondering at what skill rank does it become more beneficial to reroll rather than bump the skill rank. Here's what I have worked out, but I'm hoping someone can confirm this for me.
For case 1 (bumping the rank by 4), the probability of succeeding becomes S = (n+4)/20.
Case 2 is where I am having trouble. Do I treat these events as independent? It doesn't seem like I should. I arranged the results in a sample space and come up with 400 possible results. To find the number of results that would give a success, I found this relationship, n(40-n), so therefore the chance of success would be S = (n(40-n))/400. Using this I get the following results...
(Rank/% Chance to Succeed Using Reroll)
1/9.75
2/19
3/27.75
4/36...
Comparing this to the results from case 1, it seems that once you have acheived rank 6 or higher it is more beneficial to reroll.
Does this make sense to any stats monkeys among us? Thanks for any help you can provide.
In the game we are playing, characters may have a skill rank ranging from 1 to 20
, and to suceed at a task, the player must roll at or below his skill rank on a d20. Therefore the chance of success (S) for an event is S = n/20.Now, during the game, a player may spend a hero point to either...
1) add +4 to his original skill level or
2) reroll a failed roll
I'm wondering at what skill rank does it become more beneficial to reroll rather than bump the skill rank. Here's what I have worked out, but I'm hoping someone can confirm this for me.
For case 1 (bumping the rank by 4), the probability of succeeding becomes S = (n+4)/20.
Case 2 is where I am having trouble. Do I treat these events as independent? It doesn't seem like I should. I arranged the results in a sample space and come up with 400 possible results. To find the number of results that would give a success, I found this relationship, n(40-n), so therefore the chance of success would be S = (n(40-n))/400. Using this I get the following results...
(Rank/% Chance to Succeed Using Reroll)
1/9.75
2/19
3/27.75
4/36...
Comparing this to the results from case 1, it seems that once you have acheived rank 6 or higher it is more beneficial to reroll.
Does this make sense to any stats monkeys among us? Thanks for any help you can provide.
